Vol. 10, No. 2, 2021

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Bounding the difference of two singular moduli

Yulin Cai

Vol. 10 (2021), No. 2, 95–110
Abstract

For a fixed singular modulus α, we give an effective lower bound of the norm of x α for another singular modulus x with large discriminant. We then generalize this result for Φm(x,α), where Φm(X,Y ) [X,Y ] is the m-th modular polynomial.

Keywords
difference of singular moduli
Mathematical Subject Classification
Primary: 11F03
Milestones
Received: 25 April 2020
Revised: 3 March 2021
Accepted: 23 March 2021
Published: 23 June 2021
Authors
Yulin Cai
Institut de Mathématiques de Bordeaux
Université de Bordeaux 351
Talence
France